Analysis of lipid surface area in protein-membrane systems combining voronoi tessellation and monte carlo integration methods

All-atom molecular dynamics (MD) simulation has become a powerful research tool to investigate structural and dynamical properties of biological membranes and membrane proteins. The lipid structures of simple membrane systems in recent MD simulations are in good agreement with those obtained by experiments. However, for protein-membrane systems, the complexity of protein-lipid interactions makes investigation of lipid structure difficult. Although the area per lipid is one of the essential structural properties in membrane systems, the area in protein-membrane systems cannot be computed easily by conventional approaches like the Voronoi tessellation method. To overcome this limitation, we propose a new method combining the two-dimensional Voronoi tessellation and Monte Carlo integration methods. This approach computes individual surface areas of lipid molecules not only in bulk lipids but also in proximity to membrane proteins. We apply the method to all-atom MD trajectories of the sarcoplasmic reticulum Ca ²⁺-pump and the SecY protein-conducting channel. The calculated lipid surface area is in agreement with experimental values and consistent with other structural parameters of lipid bilayers. We also observe changes in the average area per lipid induced by the conformational transition of the SecY channel. Our method is particularly useful for examining equilibration of lipids around membrane proteins and for analyzing the time course of protein-lipid interactions.